We are collecting here answers to frequently asked questions. Contributions welcome!
If you have a Python function that changes behavior after using jax.jit, perhaps your function uses global state, or has side-effects. In the following code, the impure_func uses the global y and has a side-effect due to print:
y = 0
# @jit # Different behavior with jit
def impure_func(x):
print("Inside:", y)
return x + y
for y in range(3):
print("Result:", impure_func(y))Without jit the output is:
Inside: 0
Result: 0
Inside: 1
Result: 2
Inside: 2
Result: 4and with jit it is:
Inside: 0
Result: 0
Result: 1
Result: 2For jax.jit, the function is executed once using the Python interpreter, at which time the Inside printing happens, and the first value of y is observed. Then, the function is compiled and cached, and executed multiple times with different values of x, but with the same first value of y.
Additional reading:
Sometimes users are surprised by the fact that wrapping a function with jit can make its outputs slightly different. For example:
>>> from jax import jit >>> def f(x, y): ... return x + y - x >>> x = jnp.array(1.0) >>> y = jnp.array(0.001) >>> print(f(x, y)) 0.0010000467
>>> print(jit(f)(x, y)) 0.001
This happens because of optimizations within the XLA compiler. During compilation, XLA will often re-arrange floating point operations to simplify the expression it computes. For example, consider the expression x + y - x above. In non-JIT op-by-op evaluation, this addition and subtraction both accumulate standard 32-bit floating point arithmetic error, so the result is not exactly equal y. By contrast, in JIT the XLA compiler recognizes that the x and -x cancel each other, and so it drops these terms and the return value is identically equal to y.
In general, for this and other related reasons, it is to be expected that JIT-compiled code will produce slightly different outputs than its non-JIT compiled counterpart.
If your jit decorated function takes tens of seconds (or more!) to run the first time you call it, but executes quickly when called again, JAX is taking a long time to trace or compile your code.
This is usually a sign that calling your function generates a large amount of code in JAX's internal representation, typically because it makes heavy use of Python control flow such as for loops. For a handful of loop iterations, Python is OK, but if you need many loop iterations, you should rewrite your code to make use of JAX's structured control flow primitives (such as lax.scan) or avoid wrapping the loop with jit (you can still use jit decorated functions inside the loop).
If you're not sure if this is the problem, you can try running jax.make_jaxpr on your function. You can expect slow compilation if the output is many hundreds or thousands of lines long.
Sometimes it isn't obvious how to rewrite your code to avoid Python loops because your code makes use of many arrays with different shapes. The recommended solution in this case is to make use of functions like jax.numpy.where to do your computation on padded arrays with fixed shape. The JAX team is exploring a "masking" transformation to make such code easier to write.
If your functions are slow to compile for another reason, please open an issue on GitHub.
Let's first look at the principles of data and computation placement in JAX.
In JAX, the computation follows data placement. JAX arrays have two placement properties: 1) the device where the data resides; and 2) whether it is committed to the device or not (the data is sometimes referred to as being sticky to the device).
By default, JAX arrays are placed uncommitted on the default device (jax.devices()[0]), which is the first GPU or TPU by default. If no GPU or TPU is present, jax.devices()[0] is the CPU. The default device can temporarily overridden with the jax.default_device context manager, or set for the whole process by setting the environment variable JAX_PLATFORMS or the absl flag --jax_platforms to "cpu", "gpu", or "tpu" (JAX_PLATFORMS can also be a list of platforms, which determines which platforms are available in priority order).
>>> from jax import numpy as jnp >>> print(jnp.ones(3).device_buffer.device()) # doctest: +SKIP gpu:0
Computations involving uncommitted data are performed on the default device and the results are uncommitted on the default device.
Data can also be placed explicitly on a device using jax.device_put with a device parameter, in which case the data becomes committed to the device:
>>> import jax >>> from jax import device_put >>> print(device_put(1, jax.devices()[2]).device_buffer.device()) # doctest: +SKIP gpu:2
Computations involving some committed inputs will happen on the committed device and the result will be committed on the same device. Invoking an operation on arguments that are committed to more than one device will raise an error.
You can also use jax.device_put without a device parameter. If the data is already on a device (committed or not), it's left as-is. If the data isn't on any device—that is, it's a regular Python or NumPy value—it's placed uncommitted on the default device.
Jitted functions behave like any other primitive operations—they will follow the data and will show errors if invoked on data committed on more than one device.
jnp.device_put(jnp.zeros(...), jax.devices()[1]) or similar will actually create the array of zeros on jax.devices()[1], instead of creating the array on the default device then moving it. This is thanks to some laziness in array creation, which holds for all the constant creation operations (ones, full, eye, etc).
(As of April 2020, jax.jit has a device parameter that affects the device placement. That parameter is experimental, is likely to be removed or changed, and its use is not recommended.)
For a worked-out example, we recommend reading through test_computation_follows_data in multi_device_test.py.
You just ported a tricky function from NumPy/SciPy to JAX. Did that actuallly speed things up?
Keep in mind these important differences from NumPy when measuring the speed of code using JAX:
JAX code is Just-In-Time (JIT) compiled. Most code written in JAX can be written in such a way that it supports JIT compilation, which can make it run much faster (see To JIT or not to JIT). To get maximium performance from JAX, you should apply
jax.jiton your outer-most function calls.Keep in mind that the first time you run JAX code, it will be slower because it is being compiled. This is true even if you don't use
jitin your own code, because JAX's builtin functions are also JIT compiled.- JAX has asynchronous dispatch. This means that you need to call
.block_until_ready()to ensure that computation has actually happened (seeasync-dispatch). - JAX by default only uses 32-bit dtypes. You may want to either explicitly use 32-bit dtypes in NumPy or enable 64-bit dtypes in JAX (see Double (64 bit) precision) for a fair comparison.
- Transferring data between CPUs and accelerators takes time. If you only want to measure the how long it takes to evaluate a function, you may want to transfer data to the device on which you want to run it first (see
faq-data-placement).
Here's an example of how to put together all these tricks into a microbenchmark for comparing JAX versus NumPy, making using of IPython's convenient %time and %timeit magics:
import numpy as np
import jax.numpy as jnp
import jax
def f(x): # function we're benchmarking (works in both NumPy & JAX)
return x.T @ (x - x.mean(axis=0))
x_np = np.ones((1000, 1000), dtype=np.float32) # same as JAX default dtype
%timeit f(x_np) # measure NumPy runtime
%time x_jax = jax.device_put(x_np) # measure JAX device transfer time
f_jit = jax.jit(f)
%time f_jit(x_jax).block_until_ready() # measure JAX compilation time
%timeit f_jit(x_jax).block_until_ready() # measure JAX runtimeWhen run with a GPU in Colab, we see:
- NumPy takes 16.2 ms per evaluation on the CPU
- JAX takes 1.26 ms to copy the NumPy arrays onto the GPU
- JAX takes 193 ms to compile the function
- JAX takes 485 µs per evaluation on the GPU
In this case, we see that once the data is transfered and the function is compiled, JAX on the GPU is about 30x faster for repeated evaluations.
Is this a fair comparison? Maybe. The performance that ultimately matters is for running full applications, which inevitably include some amount of both data transfer and compilation. Also, we were careful to pick large enough arrays (1000x1000) and an intensive enough computation (the @ operator is performing matrix-matrix multiplication) to amortize the increased overhead of JAX/accelerators vs NumPy/CPU. For example, if we switch this example to use 10x10 input instead, JAX/GPU runs 10x slower than NumPy/CPU (100 µs vs 10 µs).
One question users frequently attempt to answer with such benchmarks is whether JAX is faster than NumPy; due to the difference in the two packages, there is not a simple answer.
Broadly speaking:
- NumPy operations are executed eagerly, synchronously, and only on CPU.
- JAX operations may be executed eagerly or after compilation (if inside
jit); they are dispatched asynchronously (seeasync-dispatch); and they can be executed on CPU, GPU, or TPU, each of which have vastly different and continuously evolving performance characteristics.
These architectural differences make meaningful direct benchmark comparisons between NumPy and JAX difficult.
Additionally, these differences have led to different engineering focus between the packages: for example, NumPy has put significant effort into decreasing the per-call dispatch overhead for individual array operations, because in NumPy's computational model that overhead cannot be avoided. JAX, on the other hand, has several ways to avoid dispatch overhead (e.g. JIT compilation, asynchronous dispatch, batching transforms, etc.), and so reducing per-call overhead has been less of a priority.
Keeping all that in mind, in summary: if you're doing microbenchmarks of individual array operations on CPU, you can generally expect NumPy to outperform JAX due to its lower per-operation dispatch overhead. If you're running your code on GPU or TPU, or are benchmarking more complicated JIT-compiled sequences of operations on CPU, you can generally expect JAX to outperform NumPy.
In the process of transforming functions, JAX replaces some function arguments with special tracer values.
You could see this if you use a print statement:
def func(x):
print(x)
return jnp.cos(x)
res = jax.jit(func)(0.)The above code does return the correct value 1. but it also prints Traced<ShapedArray(float32[])> for the value of x. Normally, JAX handles these tracer values internally in a transparent way, e.g., in the numeric JAX primitives that are used to implement the jax.numpy functions. This is why jnp.cos works in the example above.
More precisely, a tracer value is introduced for the argument of a JAX-transformed function, except the arguments identified by special parameters such as static_argnums for jax.jit or static_broadcasted_argnums for jax.pmap. Typically, computations that involve at least a tracer value will produce a tracer value. Besides tracer values, there are regular Python values: values that are computed outside JAX transformations, or arise from above-mentioned static arguments of certain JAX transformations, or computed solely from other regular Python values. These are the values that are used everywhere in absence of JAX transformations.
A tracer value carries an abstract value, e.g., ShapedArray with information about the shape and dtype of an array. We will refer here to such tracers as abstract tracers. Some tracers, e.g., those that are introduced for arguments of autodiff transformations, carry ConcreteArray abstract values that actually include the regular array data, and are used, e.g., for resolving conditionals. We will refer here to such tracers as concrete tracers. Tracer values computed from these concrete tracers, perhaps in combination with regular values, result in concrete tracers. A concrete value is either a regular value or a concrete tracer.
Most often values computed from tracer values are themselves tracer values. There are very few exceptions, when a computation can be entirely done using the abstract value carried by a tracer, in which case the result can be a regular value. For example, getting the shape of a tracer with ShapedArray abstract value. Another example is when explicitly casting a concrete tracer value to a regular type, e.g., int(x) or x.astype(float). Another such situation is for bool(x), which produces a Python bool when concreteness makes it possible. That case is especially salient because of how often it arises in control flow.
Here is how the transformations introduce abstract or concrete tracers:
jax.jit: introduces abstract tracers for all positional arguments except those denoted bystatic_argnums, which remain regular values.jax.pmap: introduces abstract tracers for all positional arguments except those denoted bystatic_broadcasted_argnums.jax.vmap,jax.make_jaxpr,xla_computation: introduce abstract tracers for all positional arguments.jax.jvpandjax.gradintroduce concrete tracers for all positional arguments. An exception is when these transformations are within an outer transformation and the actual arguments are themselves abstract tracers; in that case, the tracers introduced by the autodiff transformations are also abstract tracers.- All higher-order control-flow primitives (
lax.cond,lax.while_loop,lax.fori_loop,lax.scan) when they process the functionals introduce abstract tracers, whether or not there is a JAX transformation in progress.
All of this is relevant when you have code that can operate only on regular Python values, such as code that has conditional control-flow based on data:
def divide(x, y):
return x / y if y >= 1. else 0.If we want to apply jax.jit, we must ensure to specify static_argnums=1 to ensure y stays a regular value. This is due to the boolean expression y >= 1., which requires concrete values (regular or tracers). The same would happen if we write explicitly bool(y >= 1.), or int(y), or float(y).
Interestingly, jax.grad(divide)(3., 2.), works because jax.grad uses concrete tracers, and resolves the conditional using the concrete value of y.
(This feature is implemented only for TPU and GPU.)
When JAX executes a computation it reserves buffers on the device for all inputs and outputs. If you know than one of the inputs is not needed after the computation, and if it matches the shape and element type of one of the outputs, you can specify that you want the corresponding input buffer to be donated to hold an output. This will reduce the memory required for the execution by the size of the donated buffer.
You achieve this by using the donate_argnums parameter to the functions jax.jit, jax.pjit, and jax.pmap. This parameter is a sequence of indices (0 based) into the positional argument list:
def add(x, y):
return x + yx = jax.device_put(np.ones((2, 3))) y = jax.device_put(np.ones((2, 3))) # Execute add with donation of the buffer for y. The result has # the same shape and type as y, so it will share its buffer. z = jax.jit(add, donate_argnums=(1,))(x, y)
If an argument whose buffer is donated is a pytree, then all the buffers for its components are donated:
def add_ones(xs: List[Array]):
return [x + 1 for x in xs]xs = [jax.device_put(np.ones((2, 3)), jax.device_put(np.ones((3, 4))] # Execute add_ones with donation of all the buffers for xs. # The outputs have the same shape and type as the elements of xs, # so they will share those buffers. z = jax.jit(add_ones, donate_argnums=0)(xs)
It is not allowed to donate a buffer that is used subsequently in the computation, and JAX will give an error because the buffer for y has become invalid after it was donated:
# Donate the buffer for `y`
z = jax.jit(add, donate_argnums=(1,))(x, y)
w = y + 1 # Reuses `y` whose buffer was donated above
# >> RuntimeError: Invalid argument: CopyToHostAsync() called on invalid bufferYou will get a warning if the donated buffer is not used, e.g., because there are more donated buffers than can be used for the outputs:
# Execute `add` with donation of the buffers for both `x` and `y`.
# One of those buffers will be used for the result, but the other will
# not be used.
z = jax.jit(add, donate_argnums=(0, 1))(x, y)
# >> UserWarning: Some donated buffers were not usable: f32[2,3]{1,0}The donation may also be unused if there is no output whose shape matches the donation:
y = jax.device_put(np.ones((1, 3))) # `y` has different shape than the output
# Execute `add` with donation of the buffer for `y`.
z = jax.jit(add, donate_argnums=(1,))(x, y)
# >> UserWarning: Some donated buffers were not usable: f32[1,3]{1,0}Buffer donation is implemented for GPU and TPU. You will get the above warning anytime you try to use donation on CPU.
If you define a function using where to avoid an undefined value, if you are not careful you may obtain a NaN for reverse differentiation:
def my_log(x):
return jnp.where(x > 0., jnp.log(x), 0.)
my_log(0.) ==> 0. # Ok
jax.grad(my_log)(0.) ==> NaNA short explanation is that during grad computation the adjoint corresponding to the undefined jnp.log(x) is a NaN and it gets accumulated to the adjoint of the jnp.where. The correct way to write such functions is to ensure that there is a jnp.where inside the partially-defined function, to ensure that the adjoint is always finite:
def safe_for_grad_log(x):
return jnp.log(jnp.where(x > 0., x, 1.))
safe_for_grad_log(0.) ==> 0. # Ok
jax.grad(safe_for_grad_log)(0.) ==> 0. # OkThe inner jnp.where may be needed in addition to the original one, e.g.:
def my_log_or_y(x, y):
"""Return log(x) if x > 0 or y"""
return jnp.where(x > 0., jnp.log(jnp.where(x > 0., x, 1.), y)Additional reading:
See jax.errors.ConcretizationTypeError